Question

how to evaluate submission n=1 to infinity 2n+1/n^2 (n+1)^2

Answer 1

partial fractions + telescoping

Answer 2

adjust the numerator
2n+1 = \( (n+1)^2 -n^2\)

Answer 3

then separate out the denominator

Answer 4

@ganeshie8 i have did the partial but i can't get the value for A and B

Answer 5

use hartnn's hint

Answer 6

\[\dfrac{2n+1}{n^2(n+1)^2} = \dfrac{(n+1)^2 - n^2}{n^2(n+1^2)} = \dfrac{1}{n^2} - \dfrac{1}{(n+1)^2} \]

Answer 7

telescope it now